Generations III and IV

Psych Up can be stolen by Snatch, in which case Psych Up will be targeted at the (most recent) Pokémon it was stolen from.

Generation V

Psych Up can no longer be stolen by Snatch.

Generation VI onward

Psych Up now also copies the target's critical hit ratio. (e.g. If the target has the effect of Focus Energy, the user also gains that effect; if the user has the effect of Focus Energy but the target does not, the user loses that effect.)